This invention relates generally to magnetic resonance imaging (MRI), and more particularly, is directed to a method and apparatus for accurately mapping eddy currents with high resolution for use in producing a correction factor to compensate for such eddy currents.
Because of the use of x-rays with x-ray computer tomography (CT) scanning, which can be dangerous, the use of MRI or nuclear magnetic resonance (NMR) has been increasing in popularity. MRI provides safe interaction between radio frequency (RF) waves and certain atomic nuclei in the object, which may be a person, when the RF waves are placed in the presence of a strong magnetic field. Thus, MRI images can be diagnostically used in the same manner as x-rays, whereby abnormalities in the sizes and shapes of organs, and the like can be detected. In other words, with MRI, a picture image can be produced.
Specifically, MRI operates on the principle that each nucleus of protons and neutrons in certain elements, has a net spin. If the number of nuclear particles is even, their spins will cancel each other, leaving zero net spin. However, if there is an odd number of nuclear particles, a net spin other than zero will be produced. Because each nucleus is positively charged, it generates a small magnetic field when it spins. However, the magnetic moments produced by such spinning charged particles are randomly oriented.
When a magnetic field is applied, the spinning nuclei tend toward alignment with the applied field, that is, become "parallel" with the field. However, many of the nuclei do not reach perfect alignment with the field, but rather, are tilted at an angle to the field, thus behaving like tops or gyroscopes spinning under the force of gravity, that is, with the nuclei rotating or precessing in a conical manner about an axis in line with the applied magnetic field, as well as the nuclei spinning about their own axes. Thus, the nuclei have a component perpendicular to the main field known as the transverse component. The phase of this component will tend to be random. Thus, it will be appreciated that in the absence of external forces, the nuclei will tend to precess out of phase with each other.
However, the spinning nuclei eventually tend to line up in the direction of the applied magnetic field, because this is at a lower energy state. In such case, the nuclei are all in phase, that is, have phase coherence. In order for MRI to operate, the nuclei must be coherently tipped down away from such alignment toward the transverse plane, and this is accomplished by adding an RF pulse having a frequency which is the same as the natural precessional frequency of rotation of the rotating nuclei. Specifically, the RF pulse creates an RF field which rotates synchronously with the precessing spins. Accordingly, the nuclei move into a higher energy state in coherence at the resonant frequency, and thereby absorb energy. In this manner, transverse magnetization precesses around the axis of the external field, thereby inducing an AC signal, in a receiver coil, situated in a plane transverse to that of the external field. When the RF pulse is removed, the nuclei will return to the lower energy state which is in line with the magnetic field, and as they return, will emit energy. During such time, the transverse magnetization will decay to zero. Accordingly, such energy can be detected by the receiver coil in response to decay of the transverse magnetization. The signal measured externally will be the vector sum of the signal from all the individual nuclei.
In detecting the emitted RF signal, two time periods are of importance, and are termed the longitudinal relaxation time T.sub.1 and the transverse relaxation time T.sub.2. As discussed above, when the RF pulse is applied, the nuclei are in phase coherence in a plane 90.degree. offset from the plane of the external field. As soon as the applied RF pulse is terminated, the nuclei are in phase with each other. Thereafter, in the absence of the RF pulse, the nuclei become out of phase with each other. Even though the energy of the individual nuclei has not changed, the externally measured signal, which is the vector sum of the individual nuclei, will decrease due to cancellation. The time necessary for the nuclei to become out of phase with each other, is the transverse relaxation time T.sub.2.
After the lapse of time T.sub.2, the time necessary for the nuclei to again align themselves with the magnetic field is termed the longitudinal relaxation tie T.sub.1. Basically, time T.sub.2 refers to the time necessary for the nuclei to lose coherence, while the time T.sub.1 refers to the time necessary for any excess energy added by the RF pulse to totally dissipate and thereby provide for the return of the nuclei to the longitudinal state. Relaxation time T.sub.2 is always shorter, and generally considerably shorter, than relaxation time T.sub.1.
In the above discussion, time T.sub.2 is the result of both tissue properties and magnetic inhomogeneities and is more properly referred to as T.sub.2 *. The tissue T.sub.2 effects cause random changes in phase. The magnet effects produce a controlled, constant shift on phase. In normal NMR spin echo (SE) imaging, a second RF pulse, termed the 180.degree. pulse, is produced in order to invert the phase of the nuclei's signal. The interval between the first and second RF pulse is termed TE/2. If magnet effect have caused the phase to change at one point by .THETA. at time TE/2, the second RF pulse will change this to -.THETA.. Then, at time TE (the echo time), the phase will be back to zero. Thus, the magnet's effect on phase will have been cancelled. This process can be repeated with third, fourth, etc. 180.degree. RF pulses.
In regard to the above discussion, all that can be obtained from the externally measured RF signal is the amount of material that is present in the object and its mean relaxation times T.sub.1 and T.sub.2. In this regard, tissue discrimination, for example, can be provided by differences in times T.sub.1 and T.sub.2. Thus, by varying TE and TR parameters, the relative sensitivity to T.sub.1, T.sub.2 and proton density can be varied for detecting a particular tissue. However, there must also be spacial information with regard to where such object, such as an organ or the like, is located.
In this regard, an additional or gradient magnetic field is superimposed on the steady magnetic field in order to provide the spatial information. Generally, the strong steady magnetic field is applied by superconductor coils, while the gradient magnetic field is applied by resistive coils. Specifically, the gradient magnetic field is a gradually increasing or decreasing magnetic field along a given plane. Accordingly, the uniform magnetic field is modified so that it has a different value at each position of the object. Accordingly, if this gradient magnetic field is switched on during the period of data acquisition, there will be a linear variation in resonant frequency in accordance therewith.
Basically, in conventional magnetic resonance imaging, a series of two or more RF pulses and multiple gradient pulses in each of three orthogonal planes are produced concurrently in a complex fashion known as a pulse sequence. Typically, and as well known, 256 time points of data are acquired in the presence of an arbitrary x gradient of the main field in the course of each pulse sequence, thereby providing discrimination of 256 different locations along the x-axis. Simultaneously, a y magnetic gradient is used to encode each y location with a different predetermined phase. A plurality of y magnetic gradients are applied over the course of multiple phase encoding steps, with each being a complete pulse sequence, and with the complete set of all these acquisitions, y-axis resolution can be obtained. Typically, 128 different gradients or phase encoding steps will be performed. Thus, the final image will be a matrix of 32,768 (or 128.times.256) discrete points of information in the x-y plane.
In magnetic resonance imaging, from the above information, it is therefore well known to reconstruct a two-dimensional image, showing the object that has been scanned. Techniques for providing such reconstruction are well known, and are described, for example, in the book Advanced Imaging Techniques, Vol. 2, Chapter 3, "Physical Principles of Nuclear Magnetic Resonance by William G. Bradley et al., Clavadel Press, San Anselmo, CA 1983, pages 15-61; the booklet "Basic Principles of Magnetic Resonance Imaging" by Info-Scripts, Houston, Texas, 1986; a booklet "NMR A perspective on imaging" by General Electric Company, Medical Systems Group, Milwaukee, Wisconsin 53201, 1984; the text from a talk on "NMR in Medicine: A Brief Historical Review and Prospectus" by Paul C. Lauterbur, Department of Chemistry and Radiology, S.U.N.Y. at Stony Brook, given at the 4th annual conference on Integrated Body Imaging, Tokyo, Japan, Aug. 7-8, 1981; and the book Magnetic Resonance Imaging, Chapter 4, "Instrumentation" by David D. Stark et al, The C.V. Mosby Co., 1988, pages 56-65. The entire disclosures of all of the above references are incorporated herein by reference.
However, a problem occurs with eddy currents in magnetic resonance imaging. Such eddy currents are produced due to the presence of rapidly changing magnetic gradients, which occur normally with magnetic resonance imaging. Specifically, these gradient changes induce eddy currents in conductive surfaces which can exist either within the different coils or adjacent thereto. Accordingly, these eddy currents generate time and positional dependent fluctuations in the magnetic field, and thereby represent errors in the desired field distribution. See Page 59 of the Stark et al reference discussed above.
It will be appreciated that eddy current induced field errors have a sinister effect on all MRI techniques. Specifically, magnetic resonance imaging assumes that the magnetic field is in a well-defined state at every point in time. Violation of this assumption leads to improperly shaped slices and accumulated phase errors. As a result, artifacts will be produced, along with a loss of contrast in the image.
Accordingly, various systems have been proposed for compensating for such eddy current errors. Generally, in commercial MRI systems, compensation is provided by shaping the characteristics of the gradient amplifier used to produce the gradient magnetic field. Such compensation is provided by a complex feedback loop. This method is both difficult to adjust and cannot completely cancel all linear errors. An example of such a system is disclosed in the article "Reduction of pulsed gradient settling time in the superconducting magnet of a magnetic resonance instrument" in the periodical "Medical Physics", by Jensen et al, Vol. 14, No. 5, September/October 1987, pages 859-862. Other references which discuss eddy currents in NMR imaging are found in the article "Real-Time Movie Imaging from a Single Cardiac Cycle by NMR" by B. Chapman et al in the periodical "Magnetic Resonance in Medicine, 5, pages 246-254 (1987) in which the characteristics of the gradient amplifiers are modified by a filter; and the article "Exact Temporal Eddy Current Compensation in Magnetic Resonance Imaging Systems" by Michael A. Morich et al in the periodical "IEEE Transactions on Medical Imaging", Vol. 7, No. 3, September 1988, pages 247-254 in which eddy currents are compensated by a time-varying polynomial from a single sense coil using a matrix analysis. Another article relating NMR gradient behavior is found in "A General Method of Design of Axial and Radial Shim Coils for NMR and MRI Magnet" by E.S. Bobrov in the periodical "IEEE Transactions on Magnetics", Vol. 24, No. 1, January, 1988, pages 533-536. Articles relating generally to eddy currents are "Recent Development in Eddy Current Analysis" by A. Krawczyk et al in "IEEE Transactions on Magnetics", Vol. Mag-23, No. 5, September, 1987, pages 3032-3037; "Eddy Current Transients and Forces in Cyrostat Walls of Superconducting Solenoids" by G. Ries in "IEEE Transactions on Magnetics", Vol. 24, No. 1, January, 1988, pages 516-519; and "Efficient Solving Techniques of Matrix Equations for Finite Element Analysis of Eddy Currents" by Nakata et al in "IEEE Transactions on magnetics", Vol. 24, No. 1, January, 1988, pages 170-173.
In order to provide such eddy current compensation, it is necessary to first map the eddy currents, and then to correct the same with, for example, such feedback compensation.
It will be appreciated that it is extremely difficult to examine eddy induced errors created by a single gradient state change. Since a typical sequence has multiple gradient pulses, it is difficult to separate the eddy affects of one from another. Further, eddy currents can last for a few seconds. Thus, the effects of a gradient pulse can linger over several excitations.
Another problem with measuring eddy currents is the small size of their effects compared to the overall signal. Thus, an effective mapping technique needs to be able to separate eddy current effects from all other effects, and yet produce results that are distinguishable from noise.
According to one known system for mapping eddy currents, two sense coils parallel to a particular gradient axis have been provided. The outputs from the two sense coils are subtracted and then integrated to produce an output which is a time-varying representation of the linear component of the gradient field and which can be used to compensate for eddy currents so that the gradient field approaches the desired shape. However, this system has various disadvantages.
First, there are only two coils, and accordingly, the magnetic field is only sampled at two points. Thus, the change in magnetic field is represented by a linear slope extending through the two coils. However, such change in the magnetic field is generally not linear, and for example, may include higher order terms. Therefore, an accurate representation of the changes in the magnetic field cannot be determined. In order to be truly accurate, this method would require a prohibitively large number of coils. However, because of space requirements, such large number of coils could not be accommodated, and in addition, would themselves influence the field.
Secondly, there is difficulty in setting up the two coils. Generally, a separate test fixture containing the coils is required, and such set-up time may take upwards of one hour, while the measurement time may take upwards of seven hours. This means that the apparatus must be shut down during this time. It will be appreciated that MRI apparatus generally results in revenue up to and possibly more than two thousand dollars per hour, and accordingly, such loss of time results in a great loss of revenue.
A technique for creating higher resolution maps of eddy currents has recently been proposed by Y.S. Kim and Z.H. Cho in an article "Eddy-Current-Compensated Field-Inhomogeneity Mapping in NMR Imaging" published in the Journal of Magnetic Resonance, pages 459-471, 1988, the entire disclosure of which is incorporated herein by reference. Accordingly to Kim and Cho, a third dimension representing eddy-induced errors is phase encoded. Accordingly, they provide an indication of the complex nature of eddy currents. However, the spatial resolution with this method is limited by the number of eddy phase steps, and in addition, because it is a three dimensional technique, it is extremely time consuming.